Gardening Fungi
With the point of view chosen, some cleaning up of both the fungus and its immediate environment is often required.
Gliophorus viridisThe removal of unneeded, damaged or rotten fungi is a good start. Keeping in mind the rule of odds, with one, three, and five fungi in one photo being better than two, four, and six. It's not like you always have a choice, but occasionally you do.
Don't be tempted to move an adjacent fungus into the frame unless you are very careful; it is likely to stick out like a sore thumb. Some of the giveaways are from published photos where this has been done badly.

1: The species involved don't grow in tight groups, so knowing their growth form helps to avoid this mistake, even though it's not obvious to most people.

2: Fungi are sensitive to gravity and will always grow with their gills on the horizontal plane. It takes a lot of care to get a mushroom to sit right after being moved and match others in the group.

3:Fingerprints or damage to their stalks where they have been pulled from the ground and then re-planted. Care is needed to insure this does not happen with some species. It is next to impossible due to scale or glutinus stipes.

4: It is frequently difficult to move fungi without causing disruption to the ground in and around the group of fungi.

It is rare to find a fungus that does not have some dirt or leaf litter on it. Cleaning this off the fungus is in reality a two part operation. Out in the field, try to clean off as much debris from the fungus as possible. A small pair of jewellers forceps and a soft brush can be useful. Once you are back home, you can also digitally clean up your image, making extensive use of the cloning tool in a graphics editor.
Are there any twigs or other leaf debris creating bright spots of colour or reflecting light? If so, then either remove or cover these with a dead leaf or similar. Worse, twigs create lines leading out of the frame, which should be removed or covered if possible.
What about the foreground? Does it have the same problem as mentioned above? Watch out for twigs, grass, and leaf litter that are out of focus. It's best to remove it. Out of focus objects in the foreground can be very distracting, although sometimes they can help lead the eyes into the main image.
Light Spots
Look out for spots of light that occur when sunlight filters through the trees as well as direct sunlight, as these can cause unnecessary contrast. Also, bright spots reflect off shiny objects, particularly if they are wet in the background. Placing an object to block the sun's light or removing shiny objects can solve these problems.
To much
Amanita nothofagiSome careful thought needs to go into your gardening. Removing too much can result in a fungi sitting in a stark non-descriptive location. Fungi are closely tied to their habitats. Photographing one means photographing both. Adjacent leaf litter also helps to give a sense of scale to your image..
Adding extra
Hygrocybe elegans I'll admit that this is a trick I picked up from another photographer (thanks, John), and it never occurred to me before. Don't be shy about adding extra props! This can be in the form of a kauri snail shell, a bit of lichen or an interesting leaf. Caution needs to be used as you don't want to distract from the subjects, but these can help fill in an otherwise empty image.